Finite Group Databasebeta

← #24912964

Subgroups — #24912964

Order 10624.

398 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19127635C211yesmaximal, characteristic, complemented
2#19127630C211yesmaximal, characteristic
3#19127625C211yesmaximal, characteristic
4#19127598C211yesmaximal, characteristic, complemented
5#19127593C211yesmaximal, characteristic
6#19127593C211yesmaximal, characteristic
7#19127590C211yesmaximal, characteristic
8#19127590C211yesmaximal, characteristic
9#19127590C211yesmaximal, characteristic
10#19127586C211yesmaximal, characteristic, complemented
11#19127584C211yesmaximal, characteristic, complemented
12#19127583C211yesmaximal, characteristic, complemented
13#19127552C211yesmaximal, characteristic, complemented
14#19127552C211yesmaximal, characteristic, complemented
15#401×C83C211yesmaximal, characteristic, complemented
16C2×C4⋊Dic83C2211yescharacteristic
17C2×C4⋊Dic83C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2211yescharacteristic
24C2×Dic83⋊C4C2211yescharacteristic
25C2×(C2×D83)⋊C4C2211yescharacteristic
26C2×(C2×D83)⋊C4C2211yescharacteristic
27C2×(C2×D83)⋊C4C2211yescharacteristic
28C2×(C2×D83)⋊C4C2211yescharacteristic
29C2×(C2×D83)⋊C4C2211yescharacteristic
30C2×(C2×D83)⋊C4C2211yescharacteristic
31C2×(C2×D83)⋊C4C2211yescharacteristic
32C2×C4×Dic83C2211yescharacteristic
33C2×C4×Dic83C2211yescharacteristic
34C2×C4×Dic83C2211yescharacteristic
35C2×C4×Dic83C2211yescharacteristic
36C2×C4×Dic83C2211yescharacteristic
37C83⋊#95C2211yescharacteristic
38C83⋊#95C2211yescharacteristic
39C83⋊#95C2211yescharacteristic
40C83⋊#95C2211yescharacteristic
41C83⋊#95C2211yescharacteristic
42C83⋊#95C2211yescharacteristic
43C83⋊#95C2211yescharacteristic
44#95×C83C2211yescharacteristic
45#95×C83C2211yescharacteristic
46#95×C83C2211yescharacteristic
47#95×C83C2211yescharacteristic
48#95×C83C2211yescharacteristic
49#95×C83C2211yescharacteristic
50#95×C83C2211yescharacteristic
51C23×D83C2311yescharacteristic
52C22×Dic83C2311yescharacteristic
53C22×Dic83C2311yescharacteristic
54C22×Dic83C2311yescharacteristic
55C22×Dic83C2311yescharacteristic
56C22×Dic83C2311yescharacteristic
57C22×Dic83C2311yescharacteristic
58C22×Dic83C2311yescharacteristic
59C4⋊Dic83—22no—
60C4⋊Dic83—22no—
61Dic83⋊C4—22no—
62Dic83⋊C4—22no—
63Dic83⋊C4—22no—
64Dic83⋊C4—22no—
65Dic83⋊C4—22no—
66Dic83⋊C4—22no—
67Dic83⋊C4—41no—
68(C2×D83)⋊C4—22no—
69(C2×D83)⋊C4—22no—
70(C2×D83)⋊C4—22no—
71(C2×D83)⋊C4—22no—
72(C2×D83)⋊C4—22no—
73(C2×D83)⋊C4—41no—
74(C2×D83)⋊C4—41no—
75C4×Dic83—22no—
76C4×Dic83—22no—
77C4×Dic83—41no—
78C4×Dic83—41no—
79C4×Dic83—41no—
80C22×C4×C83C2311yescharacteristic
81C22×C4×C83C2311yescharacteristic
82C22×C4×C83C2311yescharacteristic
83C22×C4×C83C2311yescharacteristic
84C22×C4×C83C2311yescharacteristic
85C22×C4×C83C2311yescharacteristic
86C22×C4×C83C2311yescharacteristic
87C23×C83C2411yescharacteristic
88C22×D83—21no—
89C22×D83—21no—
90C22×D83—21no—
91C22×D83—21no—
92C22×D83—21no—
93C22×D83—21no—
94C22×D83—21no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—21no—
101C2×C4×C83—21no—
102C2×C4×C83—21no—
103C2×C4×C83—21no—
104C2×C4×C83—21no—
105C2×C4×C83—21no—
106C2×C4×C83—21no—
107C2×C4×C83—21no—
108C2×C4×C83—21no—
109C2×C4×C83—21no—
110C2×C4×C83—21no—
111C2×C4×C83—21no—
112C2×C4×C83—21no—
113C2×C4×C83—21no—
114C2×C4×C83—21no—
115C2×C4×C83—21no—
116C2×Dic83—21no—
117C2×Dic83—21no—
118C2×Dic83—21no—
119C2×Dic83—21no—
120C2×Dic83—21no—
121C2×Dic83—21no—
122C2×Dic83—21no—
123C2×Dic83—21no—
124C2×Dic83—21no—
125C2×Dic83—21no—
126C2×Dic83—21no—
127C2×Dic83—21no—
128C2×Dic83—21no—
129C2×Dic83—21no—
130C2×Dic83—21no—
131C2×Dic83—21no—
132C2×Dic83#4112yes—
133C2×Dic83#4112yes—
134C2×Dic83#4112yes—
135C2×Dic83#4112yes—
136C2×Dic83#4112yes—
137C22×C83C2×#4111yescharacteristic
138C22×C83C2×#4111yescharacteristic
139C22×C83C2×#4111yescharacteristic
140C22×C83C2×#4111yescharacteristic
141C22×C83C2×#4111yescharacteristic
142C22×C83H(5,𝔽2)11yescharacteristic
143C22×C832−1+411yescharacteristic
144C2×D83—41no—
145C2×D83—41no—
146C2×D83—41no—
147C2×D83—41no—
148C2×D83—41no—
149C2×D83—41no—
150C2×D83—41no—
151C4×C83—41no—
152C4×C83—41no—
153C4×C83—41no—
154C4×C83—41no—
155C4×C83—41no—
156C4×C83—41no—
157C4×C83—41no—
158Dic83—22no—
159Dic83—22no—
160Dic83—22no—
161Dic83—22no—
162Dic83—22no—
163Dic83—41no—
164Dic83—41no—
165C2×C83#52911yescharacteristic
166C2×C83#52911yescharacteristic
167C2×C83#53911yescharacteristic
168C2×C83#55311yescharacteristic
169C2×C83#55311yescharacteristic
170C2×C83#55611yescharacteristic
171C2×C83#55611yescharacteristic
172D83—81no—
173#2594—831nomaximal, Sylow
174C83#259411yescharacteristic, complemented, Sylow
175#401D8311yescharacteristic, complemented
176#398—831no—
177#397—831no—
178#396—831no—
179#389—831no—
180#388—831no—
181#388—831no—
182#388—831no—
183#388—831no—
184#388—831no—
185#387—831no—
186#387—831no—
187#387—831no—
188C4×C4⋊C4—831no—
189C4×C4⋊C4—831no—
190C2×C4⋊C4—831no—
191C2×C4⋊C4—831no—
192C2×C4⋊C4—831no—
193C2×C4⋊C4—831no—
194C2×C4⋊C4—831no—
195C2×C4⋊C4—831no—
196C2×C4⋊C4—831no—
197C2×C4⋊C4—831no—
198C2×C4⋊C4—831no—
199C2×C22⋊C4—831no—
200C2×C22⋊C4—831no—
201C2×C22⋊C4—831no—
202C2×C22⋊C4—831no—
203C2×C22⋊C4—831no—
204C2×C22⋊C4—831no—
205C2×C22⋊C4—831no—
206C2×C42—831no—
207C2×C42—831no—
208C2×C42—831no—
209C2×C42—831no—
210C2×C42—831no—
211#95—831no—
212#95—831no—
213#95—831no—
214#95—831no—
215#95—831no—
216#95—831no—
217#95—831no—
218#95C2×D8311yescharacteristic
219#95C2×D8311yescharacteristic
220#95C2×D8311yescharacteristic
221#95C2×D8311yescharacteristic
222#95C2×D8311yescharacteristic
223#95C2×D8311yescharacteristic
224#95C2×D8311yescharacteristic
225C24—831no—
226C22×C4—831no—
227C22×C4—831no—
228C22×C4—831no—
229C22×C4—831no—
230C22×C4—831no—
231C22×C4—831no—
232C22×C4—831no—
233C22×C4C22×D8311yescharacteristic
234C22×C4C22×D8311yescharacteristic
235C22×C4C22×D8311yescharacteristic
236C22×C4C22×D8311yescharacteristic
237C22×C4C22×D8311yescharacteristic
238C22×C4C22×D8311yescharacteristic
239C22×C4C22×D8311yescharacteristic
240C4⋊C4—3321no—
241C4⋊C4—1662no—
242C4⋊C4—1662no—
243C4⋊C4—1662no—
244C4⋊C4—1662no—
245C4⋊C4—1662no—
246C4⋊C4—1662no—
247C4⋊C4—1662no—
248C4⋊C4—1662no—
249C22⋊C4—3321no—
250C22⋊C4—3321no—
251C22⋊C4—1662no—
252C22⋊C4—1662no—
253C22⋊C4—1662no—
254C22⋊C4—1662no—
255C22⋊C4—1662no—
256C42—3321no—
257C42—3321no—
258C42—3321no—
259C42—1662no—
260C42—1662no—
261C23—1661no—
262C23—1661no—
263C23—1661no—
264C23—1661no—
265C23—1661no—
266C23—1661no—
267C23—1661no—
268C23C23×D8311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—832no—
291C2×C4—832no—
292C2×C4—832no—
293C2×C4—832no—
294C2×C4—832no—
295C2×C4—1661no—
296C2×C4—1661no—
297C2×C4—1661no—
298C2×C4—1661no—
299C2×C4—1661no—
300C2×C4—1661no—
301C2×C4—1661no—
302C2×C4—1661no—
303C2×C4—1661no—
304C2×C4—1661no—
305C2×C4—1661no—
306C2×C4—1661no—
307C2×C4—1661no—
308C2×C4—1661no—
309C2×C4—1661no—
310C2×C4—1661no—
311C22—3321no—
312C22—3321no—
313C22—3321no—
314C22—3321no—
315C22—3321no—
316C22—3321no—
317C22—3321no—
318C22#41×D8311yescharacteristic
319C22#41×D8311yescharacteristic
320C22#41×D8311yescharacteristic
321C22#41×D8311yescharacteristic
322C22#41×D8311yescharacteristic
323C22#1458183811yescharacteristic
324C22#1458183911yescharacteristic
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—3321no—
333C4—3321no—
334C4—1662no—
335C4—1662no—
336C4—1662no—
337C4—1662no—
338C4—1662no—
339C2—6641no—
340C2#1912823411yescharacteristic
341C2#1912823411yescharacteristic
342C2#1912829211yescharacteristic
343C2#1912840211yescharacteristic
344C2#1912840211yescharacteristic
345C2#1912841811yescharacteristic
346C2#1912841811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#401×C83C2
prime radicalC23×D83C23
hypercenter#401D83
hypocenterC83#2594
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #401

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19127635C2semidirect
4. #19127598C2semidirect
10. #19127586C2semidirect
11. #19127584C2semidirect
12. #19127583C2semidirect
13. #19127552C2semidirect
14. #19127552C2semidirect
15. #401×C83C2semidirect
174. C83#2594semidirect
175. #401D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191276352
#191276302
#191276252
#191275982
#191275932
#191275902
#191275862
#191275842
#191275832
#191275522
#401×C832
#259483